Likelihood-Based EWMA Charts for Monitoring Poisson Count Data With Time-Varying Sample Sizes
- 29 May 2012
- journal article
- theory and-methods
- Published by Taylor & Francis Ltd in Journal of the American Statistical Association
- Vol. 107 (499), 1049-1062
- https://doi.org/10.1080/01621459.2012.682811
Abstract
Many applications involve monitoring incidence rates of the Poisson distribution when the sample size varies over time. Recently, a couple of cumulative sum and exponentially weighted moving average (EWMA) control charts have been proposed to tackle this problem by taking the varying sample size into consideration. However, we argue that some of these charts, which perform quite well in terms of average run length (ARL), may not be appealing in practice because they have rather unsatisfactory run length distributions. With some charts, the specified in-control (IC) ARL is attained with elevated probabilities of very short and very long runs, as compared with a geometric distribution. This is reflected in a larger run length standard deviation than that of a geometric distribution and an elevated probability of false alarms with short runs, which, in turn, hurt an operator's confidence in valid alarms. Furthermore, with many charts, the IC ARL exhibits considerable variations with different patterns of sample sizes. Under the framework of weighted likelihood ratio test, this article suggests a new EWMA control chart which automatically integrates the varying sample sizes with the EWMA scheme. It is fast to compute, easy to construct, and quite efficient in detecting changes of Poisson rates. Two important features of the proposed method are that the IC run length distribution is similar to that of a geometric distribution and the IC ARL is robust to various patterns of sample size variation. Our simulation results show that the proposed chart is generally more effective and robust compared with existing EWMA charts. A health surveillance example based on mortality data from New Mexico is used to illustrate the implementation of the proposed method. This article has online supplementary materials.Keywords
This publication has 23 references indexed in Scilit:
- A comparison of weighted CUSUM procedures that account for monotone changes in population sizeStatistics in Medicine, 2010
- Nonparametric Profile Monitoring by Mixed Effects ModelingTechnometrics, 2010
- Is Average Run Length to False Alarm Always an Informative Criterion?Sequential Analysis, 2008
- Surveillance Strategies for Detecting Changepoint in Incidence Rate Based on Exponentially Weighted Moving Average MethodsJournal of the American Statistical Association, 2008
- Optimal Surveillance Based on Exponentially Weighted Moving AveragesSequential Analysis, 2006
- A Reference-Free Cuscore Chart for Dynamic Mean Change Detection and a Unified Framework for Charting Performance ComparisonJournal of the American Statistical Association, 2006
- The Performance of Exponentially Weighted Moving Average Charts With Estimated ParametersTechnometrics, 2001
- Exponentially Weighted Moving Average Control Schemes: Properties and EnhancementsTechnometrics, 1990
- Monitoring Poisson Observations Using Modified Exponentially Weighted Moving Average Control ChartsCommunications in Statistics - Simulation and Computation, 1990
- Counted Data CUSUM'sTechnometrics, 1985